Many kinds of transducers have been devised for converting a variety of physical effects (acceleration, force, pressure, etc.) into corresponding movements of a transducer element with respect to one or more other fixed elements. The relative position of the moving element is a measure of the physical effect. One common method for determining the position of the moving transducer element is to measure the electrical capacitance between it and one or more fixed elements.
FIG. 1 shows a cross section of an idealized transducer having a movable plate positioned between a pair of fixed plates. The plates are flat, conductive and of equal area, and otherwise of symmetrical structure. The capacitance between the movable plate and either fixed plate is inversely proportional to their separation. Thus, the position of the movable plate can be determined by measuring the capacitances.
The performance characteristics of such a transducer can be expressed in terms of its capacitances. However, a practical transducer system includes some form of electronics to convert capacitance changes into a more useful form of information, typically voltage. This conversion itself also influences the performance characteristics of the combination.
The overall "sensitivity" of a transducer system as used herein means the change in electrical output caused by a change in physical input. Preferably, changes in output should be linearly related to changes in input. It is significant to realize that the introduction of scaling factors, such as gain, into the system do not affect the linearity.
The sensitivity of a capacitive transducer system can be considered as the product of three independent factors:
Factor 1 is the change of position (displacement) of the movable element for a change of physical input.
Factor 2 is the change of capacitance(s) for the change of position (displacement).
Factor 3 is the change of electrical output for the change of capacitance.
The first two factors relate to the characteristics of the transducer and the third to the characteristics of the electronics.
It is desirable to increase the sensitivity of the transducer so as to minimize the effects of mechanical and electronic imprecision. This can be achieved by increasing factor 1, the displacement of the movable element for a given change of physical input (for instance, by reducing the internal forces restraining the displacement), or by increasing factor 2, the change of capacitance for a given displacement (for instance, by reducing the separation between the movable element and the fixed plates), or both. Either action causes the displacement to be a larger fraction of the separation for a given change of physical input. Thus, it is desirable to maximize the quantity (displacement/separation).
The influence of each of the three factors can be appreciated by referring again to the ideal transducer of FIG. 1. It is assumed that the displacement of the movable element from the center, or null, position is proportional to the physical input (factor 1). The distance (D1-D2) is proportional to this displacement. Since, by definition, the capacitance between two parallel plates is inversely proportional to their separation, capacitance C1 is inversely proportional to D1 and capacitance C2 is inversely proportional D2 (factor 2). If the change of electrical output is made proportional to (1/C1-1/C2), factor 3, it will be proportional to the physical input. Thus, the electrical output will be zero when the physical input is zero (no displacement) and increase in direct proportion to increases of the physical input. The sensitivity, or the change of electrical output for a change of physical input, will be constant and independent of the value of the physical input. In other words, there will be zero nonlinearity. The sensitivity can be increased by increasing the quantity (displacement/separation) without introducing nonlinearity. In this idealized system, each of the three factors contributing to the linearity of the system is itself linear.
The ideal case of high sensitivity and zero nonlinearity cannot be achieved in practical transducer systems. Basic limitations exist which reduce the sensitivity and increase the nonlinearity. Further, sensitivity and nonlinearity become interrelated, and improvements of one lead to degradation of the other.
Each of the above mentioned three factors affecting sensitivity and linearity are influenced by different limitations. An example of each is described below, showing the resulting deviation from ideal performance.
A limitation affecting factor 2, the change of capacitance for a change of position, is introduced by unavoidable extraneous capacitance(s) between the movable element and the fixed capacitor plate(s). This can occur both within the transducer itself and in the external connections to the measuring electronics. The extraneous capacitance(s) are in parallel with the transducer capacitance(s) C1 and C2, creating an effective transducer capacitance which is just the sum of the two. The electronics react to this effective capacitance and are unable to separate the effects of the transducer and extraneous capacitance(s). Since the extraneous capacitance(s) do not vary in response to the position of the movable element, the relationship between the effective transducer capacitance(s) and the position of the movable element, and the corresponding physical input, is altered.
The effect of the extraneous capacitance(s) on the overall system sensitivity and linearity depends upon the electronic algorithm used for factor 3. Even if the change of electrical output for a change of capacitance is made proportional to (1/C1-1/C2), which is preferably the best choice for minimum nonlinearity, the extraneous capacitance(s) will still cause a reduction of sensitivity and an increase of nonlinearity. The sense of the nonlinearity is that the sensitivity will increase for increasing input, as shown in FIG. 2. Further, if the sensitivity is increased by increasing the quantity (displacement/separation), the nonlinearity will increase.
This effect of extraneous capacitance becomes increasingly important when the capacitance of the transducer is decreased through miniaturization, as the extraneous capacitance becomes larger with respect to the transducer capacitance.
Extraneous capacitance functions as a part of the transducer capacitance which does not respond to the physical input. In general, a limitation to ideal performance exists whenever all portions of the transducer capacitance do not respond equally to the physical input.
This limitation can affect factor 1, the change of position (displacement) of the movable element for a change of physical input, when the displacement of all regions of the movable element is not the same for changes of the physical input. This non-uniform displacement causes the sensitivity to become nonlinear, and the sense of this nonlinearity is again that the sensitivity will increase for increasing input.
An example of this limitation is the introduction of a suspension element(s) which mechanically locates the movable element with respect to the fixed elements. The displacement of the suspension element(s) will vary from full displacement at the connection to the movable element, to no displacement at the connection to the fixed elements. To the extent that the suspension element(s) are included as part of the capacitance of the sensor, the effect will be to increase the nonlinearity. The sense of the nonlinearity is that the sensitivity will increase for increasing input.
A more complex example of this limitation is the case where the movable element and its suspension elements merge into a clamped diaphragm, as shown in FIG. 3. A circular deflectable diaphragm is attached at its periphery to a fixed structure. Two capacitor plates are located with respect to the fixed structure on either side of the diaphragm at nominally equal distances. A difference of pressure is applied across the diaphragm, causing it to bend toward one fixed capacitor plate and away from the other.
Even if the displacement of every region of the diaphragm is itself directly proportional to pressure input, all regions of the diaphragm do not deflect equally. The curved diaphragm itself exhibits non-uniform displacement and thus creates a nonlinearity. It is virtually impossible to exclude the offending regions of the diaphragm from the transducer capacitance since all regions behave in this fashion. Thus, the sensitivity will be nonlinear, and the sense of this nonlinearity is again that the sensitivity will increase for increasing input.
As in the previous example, if the sensitivity is increased by increasing the quantity (displacement/separation), the nonlinearity will increase.
A limitation affecting factor 3, the change of electrical output for a change of capacitance, is introduced by the choice of the algorithm defining the conversion of transducer capacitance to electrical output. As previously shown, making the output proportional to (1/C1-1/C2) produces a linear output for an ideal transducer and is thus the best choice. If, for example, the output of an ideal transducer system were made proportional to (C1-C2), the sensitivity would be very nonlinear for significant displacements, approaching infinity as the movable plate approached one of the fixed plates. Thus, the choice of the electronic conversion algorithm significantly affects nonlinearity. As before, the sense of this nonlinearity is that the sensitivity will increase for increasing input. And as before, if the sensitivity is increased by increasing the quantity (displacement/separation), the nonlinearity will increase.
These practical limitations of performance in practical capacitance transducer systems all function to reduce sensitivity and increase nonlinearity. The sense of the nonlinearity is always an increase of sensitivity for increasing input.
The usual practice to reduce this nonlinearity is to use relatively low values of the quantity (displacement/separation); that is, to restrict the displacement of the movable element to a small fraction of the separation between the elements. Unfortunately, this also causes a reduction of sensitivity. Since nonlinearity will approach zero only when the displacement approaches zero, an attempt must be made to obtain an acceptable compromise between nonlinearity and sensitivity. As sensitivity is reduced, mechanical stability and precision become increasingly critical since the displacement for a given input is reduced. Also, electronic stability and noise become increasingly critical since the signal level for a given physical input is reduced. These problems become even more critical as the size of the transducer is reduced.
In principle, linearity can be improved by the use of compensating nonlinearities in factor 3, the conversion of changes of capacitance to changes of electrical output. However, no linear homogeneous function of the transducer capacitance(s), or ratio of such functions, will cause the sensitivity to decrease for increasing input, and thereby offset the nonlinearities described above. This forces the use of nonlinear functions, and the attendant added cost and complexity. The complexity of the required circuits increases dramatically as the accuracy of the correction increases, making this alternative practical only for transducers of moderate performance or high cost.
U.S. Pat. Nos. 4,542,436 and 4,858,097 illustrate measures taken in an attempt to reduce nonlinearities in capacitive-type sensors. In U.S. Pat. Nos. 4,054,833; 4,295,376; and 4,386,312, circuit design techniques have been implemented for either reducing nonlinearities generally inherent in sensor circuits, or for compensating for nonlinearities generated within the circuit itself.
From the foregoing, it can be seen that a need exists for a solution which provides high sensitivity and low nonlinearity without introducing additional cost or complexity.
A need also exists for a technique to obtain essentially zero nonlinearity over the performance range of the transducer, without unduly compromising the magnitude of the sensitivity.
A need also exists for a technique to obtain essentially zero nonlinearity when using non-ideal electronic conversion algorithms.
A further need exists for a technique which allows increasing the quantity (displacement/separation) without unduly compromising the magnitude of the nonlinearity.
A further need exists for a technique in which a nonlinearity of one sense can be introduced into the fabrication of the transducer device to offset the inherent nonlinearities of the opposite sense due to the effects of extraneous capacitance, non-uniform displacement and non-ideal electronic conversion algorithms.